## Foundations of Vietoris homology theory with applications to non-compact spaces |

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### Contents

Preface | 5 |

HI Sequential chains | 17 |

Functions mappings and null translations | 25 |

Copyright | |

2 other sections not shown

### Common terms and phrases

abelian group abstract n-dimensional Alexandroff dimension theorem Alexandroff equivalence algebraic topology Borsuk boundary operator carrier X0 closed locally compact closed subsets closed subspace commutes compact metric space compact set X0 compact subset compactly dimensioned cycles and boundaries define a function denoted dimensional compact metric dimensional metric space e-chains e-simplex essential cycle exists finite dimensional metric fj(x hence Hilbert cube homomorphism f homotopy theorem induces a homomorphism infinite chain infinite cycle isomorphic lemma Let X,g locally compact space locally compact subspaces locally countable union locally finite Math Moreover null translation Proof proved quotient group satisfies the Alexandroff sequence sequential chains simple chains simplex space is compactly space with dim spaces and let Theorem 11 Theorem 30 Theorem 42 Topological invariance topological space translation with majorant true cycle union of locally vertices Vietoris homology groups Vietoris homology theory Vietoris theory X0 n y0